Considered here are production (or market) games with transferable utility. Prime objects are explicitly computable core solutions, or somewhat "deficit" versions of such, fully defined by shadow prices. Main arguments revolve around standard Lagrangian duality. A chief concern is to relax, or avoid, the commonplace assumption that all preferences and production possibilities be convex. Doing so, novel results are obtained about non-emptiness of the core, and about specific imputations therein.